quite
"proper" mathematically, it is usuallycustomary
to change it to a mixed number. Arecipe may
call for 1 1/2 cups of milk, but wouldnot
call for 3/2 cups of milk.

Since a fraction is an indicated division, a

method
is already known for reduction of improper fractions to mixed numbers. The
improper fraction 8/3 may be considered as the division of 8. by 3. This
division is carried outas follows:

The truth of this can be verified another way:

If 1 equals 3/3 then 2 equals 6/3 Thus,

These examples lead to the following conclusion, which is stated as a rule:
To change

an improper fraction to a mixed
number, dividethe numerator by the
denominator and write thefractional part of
the quotient in lowest terms.

Practice problems. Change the following

fractions
to mixed numbers:

1. 31/20
2. 33/9
3. 65/20
4. 45/8

Answers :

OPERATING WITH MIXED NUMBERS

In computation, mixed numbers are often unwieldy. As it is possible to change
any improper fraction to a mixed number, it is like- wise
possible to change any mixed number to animproper
fraction. The problem can be reducedto the
finding of an equivalent fraction and asimple
addition.

In each of these examples, notice that the multiplier
used in step 2 is the same number asthe
denominator of the fractional part of theoriginal
mixed number. This leads to the following conclusion, which is stated as a rule:To change a mixed number to an improper fraction,
multiply the whole-number part by thedenominator
of the fractional part and add thenumerator
to this product. The result is thenumerator
of the improper fraction; its denominator is the same as the denominator of thefractional part of the original mixed number.

A fraction preceded by a minus sign is negative. Any negative fraction is
equivalent to a positive fraction multiplied
by -1. For example,

The number -2/5 is read "minus two-fifths."

We know that the quotient of two numbers with
unlike signs is negative. Therefore,

This indicates that a negative fraction is equivalent to a fraction with
either a negative numerator or a negative denominator. The
fraction 2/-5 is read "two over minusfive."
The fraction 3 is read "minus twoover
five."

A minus sign in a fraction can be moved about
at will. It can be placed before the numerator, before the denominator, or
before thefraction itself. Thus,

Moving the minus sign from numerator to denominator,
or vice versa, is equivalent tomultiplying
the terms of the fraction by -1.This is
shown in the following examples:A fraction
may be regarded as having threesigns
associated with it-the sign of the numerator, the sign of the denominator, and
the signpreceding the fraction. Any two of
these signsmay be
changed without changing the value ofthe
fraction. Thus,

OPERATIONS WITH FRACTIONS

It will be recalled from the discussion of denominate
numbers that numbers must be ofthe same
denomination to be added. We can addpounds
to pounds, pints to pints, but not ouncesto
pints. If we think of fractions loosely as denominate numbers, it will be seen
that the ruleof likeness applies also to
fractions. We canadd eighths to eighths,
fourths to fourths, butnot eighths to
fourths. To add 1/5 inch to 2/5 inchwe
simply add the numerators and retain thedenominator
unchanged. The denomination isfifths; as
with denominate numbers, we add 1fifth to 2
fifths to get 3 fifths, or 3/5.